“Is there anything in the Bible that might allow for same-sex marriage?”—Mark

First, let’s be clear that there are indeed various forms of marriage found in scripture that may not meet the definition of what is often called the “traditional family” (e.g., multiple wives, Levirate marriage, concubinage, close degrees of familial relationship i.e., marriage between half-siblings, cousins, et al).
Furthermore, wedding “ceremonies,” as we moderns practice them, do not appear in scripture. Arranged marriages and politically and religiously motivated unions were commonly accepted practices in biblical times.
On one point, however, the Bible is unabashedly straightforward: the ideal for marriage is heterosexual; i.e., one man and one woman for life in a “one-flesh” relationship (Gen. 2:24).
This statement reflects a deeper truth: maleness and femaleness are subsumed in the image of God (Gen. 1:26ff). The intimate connectedness of male and female in every dimension of their relationship and responsibility in the world (regarding both procreation and stewardship of the Earth, Gen. 1:27) finds its basis in his very nature as the creative, purposeful, triune God.
This is not to say that two people who define themselves as having a homosexual orientation cannot love each other or be committed to one another.
This is to say that such a homosexual relationship does not, by definition, fulfill the biblical understanding of the intent and purposes of the one-flesh (heterosexual) union.
Simply put, husband (male) and wife (female) are assumed as “the norm” for marriage throughout the Bible (see, for example, Dt. 20:7; Pr. 18:22; 31; I Cor. 7:1-16; Eph. 5:22-33; I Tim. 5:1-16; Heb.13:4).
As much as you might wish otherwise, you cannot construct a valid argument to support same-sex marriage from the Bible (see the “holiness code” of Leviticus 18; 20; see also Rom. 1:18ff; I Cor. 6:9ff; I Tim. 1:8-11).